1. Field
The present disclosure generally relates to random estimation in Positron Emission Tomography (PET) reconstruction.
2. Background
The most accurate and commonly used method for random estimation in Positron Emission Tomography (PET) reconstruction is the delayed coincidence window estimation, in which the correlation between the paired photons generated from a single annihilation can be totally removed, thus leaving only random events. However, due to the limited coincidence window and short acquisition time, statistically, the measured delay data is only one realization of the true random data distribution. Therefore, if not processed properly, the variance will increase in the prompt data after subtracting the delayed coincidence window data.
There are many image smoothing techniques developed in a uniformly sampled data space, such as Fourier analysis, to remove high frequency noise. The directly acquired delay raw sinogram, however, is not in a uniformly sampled space. If the delay raw sinogram could be converted into a uniformly sampled interpolated-sinogram, then various standard smoothing techniques could be used. The data could then be back-interpolated to the irregular-sampled raw sinogram space after random sinogram smoothing in the uniformly interpolated-sinogram space.
Noise represents the high frequency components in the spectrum of the noisy random sinogram. Random sinogram smoothing can be applied by filtering out the high frequencies in the Fourier domain. But the smoothing will also cause large changes in the signals that are present in the random sinogram distribution. Furthermore, the Fourier method is a global representation of the signal and will fail for images with an irregular mask, as in the case of random sinogram smoothing in which the interpolated random sinogram is restricted inside a mask containing all the measurable line-of-responses. The mask represents the measurable region in the image. Thus, any region outside the mask will not be measurable and thus have pixel intensity of zero.